Let ABCDABCDABCD be a rectangle such that AB=5AB=5AB=5 and BC=12BC=12BC=12. There exist two distinct points X1X_1X1 and X2X_2X2 on BCBCBC such that ∠AX1D=∠AX2D=90∘\angle AX_1D=\angle AX_2D=90^\circ∠AX1D=∠AX2D=90∘. Suppose that ddd is the distance from X1X_1X1 to X2X_2X2. What is d2d^2d2?
This problem is posed by David A.